Question: Rewrite as a simplified fraction. ${1.59\overline{2} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 1592.2222...\\ 100x &= 159.2222...\end{align*}}$ Subtracting the two equations, we have: ${900x = 1433}$ ${x = \dfrac{1433}{900}} \text{or} {1 \dfrac{533}{900}}$